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I have a products that can be in multiple categories, example take a look at the following strings:

• Cat1>Product1


• Cat1>Product2


• Cat2>subcat1>Product1


• Cat3>subcat1>subcat2>Product1

In woocommerce, if I have a productid, I can do the following:

 function alg_product_categories_names2( $atts ) 
 $product_cats = get_the_terms( $this->get_product_or_variation_parent_id( $this->the_product ), 'product_cat' );
 $cats = array();

 $termstest= '';
 if ( ! empty( $product_cats ) && is_array( $product_cats ) ) 
 foreach ( $product_cats as $product_cat ) 
 if ( $term->parent == 0 ) //if it's a parent category
 $termstest .= ' PARENTCAT= '. $product_cat->name;
 
 
 

 return htmlentities('<categories_names>'. $termstest .'</categories_names>');

But this simply returns all the parent categories for the product id.

cat1, cat2, subcat1, Cat3, subcat2

I'm having a hard time with this. What I need is given a product id, build the list above - what should be returned is:

"Cat1>Product1" | "Cat2>subcat1>Product1" | "Cat3>subcat1>subcat2>Product1"

I basically need to rebuild each category path from the product id.

To get all ancestors of a product category, you can use the Wordpress get_ancestors() function

The following custom shortcode function will output for each product category of a given product, the ancestors with the product category in a string as defined in your question:

add_shortcode( 'product_cat_list', 'list_product_categories' )
function list_product_categories( $atts )
 $atts = shortcode_atts( array(
 'id' => get_the_id(),
 ), $atts, 'product_cat_list' );

 $output = ; // Initialising
 $taxonomy = 'product_cat'; // Taxonomy for product category

 // Get the product categories terms ids in the product:
 $terms_ids = wp_get_post_terms( $atts['id'], $taxonomy, array('fields' => 'ids') );

 // Loop though terms ids (product categories)
 foreach( $terms_ids as $term_id ) 
 $term_names = ; // Initialising category array

 // Loop through product category ancestors
 foreach( get_ancestors( $term_id, $taxonomy ) as $ancestor_id )
 // Add the ancestors term names to the category array
 $term_names = get_term( $ancestor_id, $taxonomy )->name;
 
 // Add the product category term name to the category array
 $term_names = get_term( $term_id, $taxonomy )->name;

 // Add the formatted ancestors with the product category to main array
 $output = implode(' > ', $term_names);
 
 // Output the formatted product categories with their ancestors
 return '"' . implode('" 

Code goes in function.php file of your active child theme (active theme). Tested and works.

USAGE:

1) In the php code of product page:

echo do_shortcode( "[product_cat_list]" );

2) In php code with a given product ID (here the product ID is 37 for example):

echo do_shortcode( "[product_cat_list id='37']" );

I think that the product name is not needed in your output as it is repetitive (on each product category). So you will get something like this:

"Cat1" | "Cat2>subcat1" | "Cat3>subcat1>subcat2"